[cosmodisk]

Drop them. If some corporate cog thinks having you on a speed dial 27/7 is a good idea, just because they pay, you definitely don't want them as clients. Instead, tell them you are awesome, your product is the hottest shit in town and you work 4 days a week. The language may vary depending on a client, but setting boundaries is part of the game.

[atatatat]

Just "business hour" support can take you out of eligibility to (morally) accept a role at another firm.

[icedchai]

Morally, maybe, but not practically. You can send emails or answer the phone during your regular job. The odds of you being "caught" are near zero.